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+1 vote
34.3k views
in Mathematics by (63.5k points)

Show that the points A(-2i + 3j + 5k), B(i + 2j + 3k), C(7i - k) are collinear.

1 Answer

+2 votes
by (64.8k points)
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Best answer

We have

vector AB = (1 + 2)i + (2 - 3)j + (3 - 5)k = 3i - j - 2k

vector BC = (7 - 1)i + (0 - 2)j + (-1 - 3)k = 6i - 2j - 4k

vector CA = (7 + 2)i + (0 - 3)j + (-1 - 5)k = 9i - 3j - 6k

Now, |vector AB|2 = 14, |vector BC|2 = 56, |vector CA|2 = 126

⇒ |vector AB| = √14, |vector BC| = 2√14, |vector CA| = 3√14

⇒ |vector CA| = | vector AB| + |vector BC|

Hence the points A, B and C are collinear.

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